Page 91 - Formation Damage during Improved Oil Recovery Fundamentals and Applications

Formation Damage by Fines Migration: Mathematical and Laboratory Modeling, Field Cases 73

Kinetic Eq. (3.2) is analogous to the equation for nonequilibrium
adsorption, where adsorption and desorption occur simultaneously.
Equilibrium sorption corresponds to an equality of the adsorbed and des-
orbed rates. The rate expression for nonequilibrium adsorption reflects
interface mass transfer that is proportional to the difference between
Gibbs potentials of suspended and adsorbed matter. However, the work
of the dissipative drag force F d that is present in the condition of mechan-
ical equilibrium Eq. (3.1) cannot be included into an energy potential,
resulting in velocity-dependent attached concentration.
Kinetics Eq. (3.2) does not reflect the mechanical equilibrium condi-
tion expressed by Eq. (3.1). The filtration function can be derived by
averaging of microscale flow in a pore, although the detachment coeffi-
cient is purely phenomenological and cannot be derived from micro-
scopic physics.
On the contrary to the abovementioned shortcomings of Eq. (3.2),
the modified particle detachment model follows from the torque balance
condition of mechanical equilibrium Eq. (3.1). Consider an ensemble of
particles on the rock surface, and apply the flow with given velocity U,
ionic strength γ, pH, temperature T, etc. For each particle, Eq. (3.1)
makes it possible to define whether the particle is attached to the rock or
lifted by the detaching torques. The particles submitted to detaching tor-
ques, which exceed the attaching torque defined by the maximum elec-
trostatic attraction, are mobilized. It makes the attached concentration of
remaining fines a function of velocity U, ionic strength, pH, temperature
T, etc., which is called the maximum retention function (Bedrikovetsky
et al., 2011a; 2012; You et al., 2016; Yuan et al., 2016).
The interface mass transfer by particles between the solid and fluid
becomes:

λcU; σ a , σ cr U; γÞ
(
ð
@σ a
5 ; (3.3)
@t
σ a 5 σ cr U; γð Þ; σ a 5 σ cr U; γÞ
ð
i.e., the particles attach until reaching the maximum retention value, and
afterward the attached concentration remains equal to the maximum
retention function. Continuous particle detachment during flows with
decreasing salinity or increasing velocity and pH corresponds to the sec-
ond line of Eq. (3.3), where time variations of U, γ, pH, and T result in a
decrease of the maximum retention function.
The above fines-lifting mechanisms are supported by the typical skin
histories for production wells in the Campos Basin (Brazil), presented in